A person places $7380 in an investment account earning an annual rate of
1.9%, compounded continuously. Using the formula V = Pert, where Vis
the value of the account in t years, P is the principal initially invested, e is the
base of a natural logarithm, and r is the rate of interest, determine the
amount of money, to the nearest cent, in the account after 11 years.

Answers

Answer 1

Answer: $9095.44

Step-by-step explanation:

Given:

P=7380

r=1.9% = .019

t= 11

V = P[tex]e^{rt}[/tex]                               >substitute

V = 7380 [tex]e^{(.019)(11)}[/tex]              >Plug into calculator

V= $9095.44


Related Questions

js say yes or no and 1 sentence explanation not too big

Answers

Answer:

Yeah

Owning a phone --> 198/22 = 9

Not owning a phone ---> 72/8 = 9

Total people ----> 270/30 = 9

Im not sure what ur supposed to do but for all of these when u divide the people that aren't late by the people that are late you get 9 so most probably associated

Arianna's personal residence has an adjusted basis of $300,450 and a fair market value of $270,405. Arianna converts the personal residence to rental property. What is Arianna's gain basis

Answers

If Arianna decides to sell the rental property in the future, the gain or loss will be calculated based on the $270,405 gain basis.

The gain basis for Arianna's converted personal residence to rental property can be calculated by determining the lower value between the adjusted basis and the fair market value.

In this case, the adjusted basis is $300,450 and the fair market value is $270,405.

The gain basis is the lower of the two values, which in this case is $270,405. This means that the gain basis for Arianna's rental property is $270,405.

The gain basis is important for tax purposes as it is used to calculate the taxable gain or loss when the property is eventually sold.

If the property is sold for a higher price than the gain basis, there will be a taxable gain.

On the other hand, if the property is sold for a lower price than the gain basis, there will be a deductible loss.

In Arianna's case, if she decides to sell the rental property in the future, the gain or loss will be calculated based on the $270,405 gain basis.

It is important to note that there may be additional factors and adjustments that could affect the final tax calculations, such as depreciation deductions and any improvements made to the property.

Consulting a tax professional would provide more accurate and detailed information regarding the tax implications of selling the rental property.

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NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Consider the relation (a, b) a and b have the same age) on the set of all people. Identify the properties that the given relation satisfies. (Check all that apply.) [You must provide an answer before moving to the next part.) Check All That Apply 0 0 symmetric 0 transitive 0 antisymmetric

Answers

The relation (a, b) "a and b have the same age" satisfies the following properties:

1. Symmetric: Yes.

2. Transitive: No.

3. Antisymmetric: No.

Determine the relation?

1. Symmetric: The relation is symmetric because if a is the same age as b, then b is also the same age as a. It is a two-way relationship, and the order of the elements does not matter.

2. Transitive: The relation is not transitive because if a is the same age as b, and b is the same age as c, it does not necessarily mean that a is the same age as c. The transitive property states that if aRb and bRc, then aRc, but this does not hold for the given relation.

3. Antisymmetric: The relation is not antisymmetric because there can be cases where a and b are different individuals but have the same age, violating the condition for antisymmetry, which requires that if aRb and bRa, then a = b.

In summary, the relation is symmetric but not transitive or antisymmetric.

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Which set of ordered pairs is shown in this scatter plot?

Question 17 options:

(6,4) (4,6) (1,3) (2,5) (1,6) (3,6)


(6,-4) (4,-6) (1,-3) (2,-5) (1,-6) (3,-6)


(-6,4) (-4,6) (-1,3) (-2,5) (-1,6) (-3,6)


(4,6) (6,4) (3,1) (2,5) (1,6) (3,6)

Answers

Answer:

(1, 3), (1, 6), (2, 5), (3, 6), (4, 6), (6, 4) : The first one

Hope this helps!

Step-by-step explanation:

The X - axis is horizontal and the Y - axis is vertical.

( x, y )

Solve the problem using unit Rates

Answers

[tex]\begin{array}{ccll} \stackrel{jam}{liters}&days\\ \cline{1-2} 32 & 8\\ 36& x \end{array} \implies \cfrac{32}{36}~~=~~\cfrac{8}{x} \implies \cfrac{8}{9} ~~=~~ \cfrac{8}{x}\implies 9=x[/tex]

I need the explanation and answer for this question ASAP.

Answers

If Jack cuts the rectangular sheet of paper in half, he will get two identical rectangles that are similar to the original sheet of paper. This means that the ratio of the sides of the original rectangle is the same as the ratio of the sides of each of the new rectangles.

Let's say that the longer side of the original rectangle is x cm long. Then, the shorter side is 27 cm long. When Jack cuts the rectangle in half, each of the new rectangles will have a shorter side of 27 cm and a longer side of x/2 cm.

Since the new rectangles are similar to the original rectangle, we know that the ratio of the longer side of the original rectangle to the shorter side of the original rectangle is the same as the ratio of the longer side of the new rectangle to the shorter side of the new rectangle. This can be written as:

x/27 = (x/2)/27

We can solve this equation for x:

x/27 = x/54

54x = 27x

27x = 0

x = 0

This answer doesn't make sense because the length of the longer side of the original rectangle can't be 0. The reason we got this answer is that we made a mistake in the equation. We should have written:

x/27 = 27/(x/2)

This equation can be simplified to:

x^2 = 27*54

x^2 = 1458

x = sqrt(1458)

x = 38.15 cm (rounded to 3 s.f.)

Therefore, the longer side length of the original sheet of paper is 38.15 cm (rounded to 3 s.f.).

Anderson is bakin pies. He needs 1/3 cup of butter for each pie. One stick butter is 1/2 cup.


how many sticks of butter does anderson need to make 6 pies?

Answers

Anderson needs 9 sticks of butter that are proportionate to 6 pies.


Anderson needs 1/3 cup of butter for each pie, and one stick of butter is equal to 1/2 cup.

To find the number of sticks of butter Anderson needs to make 6 pies, we can set up the following proportion:

(1/3 cup butter per pie) / (1/2 cup butter per stick) = (6 pies) / (x sticks)

To solve for x, we can cross-multiply:

(1/3) / (1/2) = 6 / x

Multiplying both sides by (1/2) to isolate x:

x = (6 * 1/2) / (1/3)

x = 3 * 3

x = 9

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a class has eight girls and two boys. if the teacher randomly picks eight students, what is the probability that she will pick all girls? find the probability of the event.

Answers

Given that a class has 8 girls and 2 boys. The teacher randomly picks 8 students. We need to find the probability that she will pick all girls.

To find the probability of the event, we need to use the formula for the probability of an event, which is:

P (event) = Number of favorable outcomes / Total number of outcomes Probability of picking all girls out of 10 studentsSince there are 8 girls and 2 boys in the class, the total number of students is 10.

There are only 8 girls, so the only way to pick all girls is if all 8 girls are selected out of the 10 students.

Total number of outcomes = 10 C8 = 45 (number of ways to pick 8 students out of 10) Number of favorable outcomes = 1 (since there is only one way to pick all 8 girls)

Therefore, the probability of the teacher picking all girls is:P (all girls) = 1/45 Thus, the probability of the teacher randomly picking all girls out of 8 girls and 2 boys is 1/45.

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an insurance company checks police records on 582 accidents selected at random and notes that teenagers were at the wheel in 91 of them. (a) (8 pts) find the 95% confidence interval for , the true proportion of all auto accidents that involve teenage drivers. (note: for full credit, show all your work. no credit

Answers

The 95% confidence interval for the true proportion of all auto accidents involving teenage drivers is approximately (0.1205, 0.1927).

To find the 95% confidence interval for the true proportion of all auto accidents involving teenage drivers, we can use the formula for the confidence interval for a proportion.

The formula for the confidence interval is:

CI = p1 ± Z * √((p1 * (1 - p1)) / n)

Where:

CI is the confidence interval,

p1 is the sample proportion (proportion of accidents involving teenage drivers),

Z is the Z-score corresponding to the desired confidence level (95% confidence level corresponds to Z ≈ 1.96),

n is the sample size (number of accidents checked).

Given:

Number of accidents checked (sample size), n = 582

Number of accidents involving teenage drivers, x = 91

First, we calculate the sample proportion:

p1 = x / n = 91 / 582 ≈ 0.1566

Now we can calculate the confidence interval:

CI = 0.1566 ± 1.96 * √((0.1566 * (1 - 0.1566)) / 582)

Calculating the standard error of the proportion:

SE = √((p1 * (1 - p1)) / n) = √((0.1566 * (1 - 0.1566)) / 582) ≈ 0.0184

Substituting the values into the formula:

CI = 0.1566 ± 1.96 * 0.0184

Calculating the values:

CI = 0.1566 ± 0.0361

Finally, we can simplify the confidence interval:

CI = (0.1205, 0.1927)

Therefore, the 95% confidence interval for the true proportion of all auto accidents involving teenage drivers is approximately (0.1205, 0.1927).

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A firm with $600,000 in sales, cash on hand of $750,000, liabilities of $200,000, and total assets of $1 million has a total asset turnover of

Answers

the firm has a total asset turnover of 0.6, which means that for every $1 of total assets, the firm generates $0.6 in sales. This ratio indicates the firm's efficiency in utilizing its assets to generate revenue

Total asset turnover is a financial ratio that measures a company's efficiency in generating sales from its total assets. It is calculated by dividing the total sales by the average total assets. In this case, the firm has $600,000 in sales and total assets of $1 million.

Total Asset Turnover = Total Sales / Average Total Assets

To calculate the average total assets, we sum the beginning and ending total assets and divide by 2:

Average Total Assets = (Beginning Total Assets + Ending Total Assets) / 2

Given that the firm's total assets are $1 million, the average total assets would also be $1 million.

Plugging in the values into the total asset turnover formula:

Total Asset Turnover = $600,000 / $1,000,000 = 0.6

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A rock that has been significantly reshaped on multiple surfaces by windborne particles and sometimes has a sharp edge is a(n) ________.

Answers

A rock that has been significantly reshaped on multiple surfaces by windborne particles and sometimes has a sharp edge is a(n)  ventifact:

What is a rock?

A rock refers to the solid portion of the earth crust which contains minerals. There are three types of rocks; The sedimentary rock: They are formed from dead plants, dead animals, sand etc.

The metamorphic rock: They are formed from previously existing rocks. The igneous rock: They are formed from the solidification of the molten magma.

Hence, ventifact are rock  that has been significantly reshaped on multiple surfaces by windborne particles and sometimes has a sharp edge.

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a garden is to be laid out in a rectangular area and protected by a chicken wire fence. what is the largest possible area of the garden if only 100 running feet of chicken wire is available for the fence? round your answer to the nearest tenth, and use correct units.

Answers

Rounding to the nearest tenth, the largest possible area of the garden is 625 square feet.

What is area of rectangle?

The area of a rectangle is a measure of the region enclosed by its four sides. It represents the amount of space or surface covered by the rectangle. The formula to calculate the area of a rectangle is:

Area = Length × Width

To find the largest possible area of the garden given a limited amount of chicken wire fence, we need to determine the dimensions of the rectangular garden that would maximize its area.

Let's assume the length of the rectangular garden is L and the width is W. The perimeter of the garden, which is the length of the chicken wire fence required, can be expressed as:

Perimeter = 2L + 2W

Given that the perimeter is 100 running feet, we have:

2L + 2W = 100

Simplifying the equation, we get:

L + W = 50

To maximize the area, we need to maximize the product of the length and width, which represents the area of the garden:

Area = L * W

We can rewrite the equation for the area in terms of one variable using the constraint L + W = 50:

Area = (50 - W) * W

To find the maximum area, we can take the derivative of the area equation with respect to W, set it equal to zero, and solve for W:

d(Area)/dW = 50 - 2W = 0

2W = 50

W = 25

Substituting the value of W back into the equation L + W = 50:

L + 25 = 50

L = 25

Therefore, the largest possible area of the garden is obtained when the length and width are both 25 feet. The maximum area is:

Area = L * W = 25 * 25 = 625 square feet.

Rounding to the nearest tenth, the largest possible area of the garden is 625 square feet.

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Assuming the heterocyclic ring above to be planar: Give the number of electrons that are contributed to the pi system of the heterocyclic ring by:

Answers

The number of electrons contributed to the pi system of a planar heterocyclic ring can be determined by counting the number of pi electrons within the ring. These pi electrons arise from the conjugated double bonds or aromaticity present in the ring structure.

In a planar heterocyclic ring, the contribution of electrons to the pi system can be determined by analyzing the presence of conjugated double bonds or aromaticity within the ring. Conjugated systems are formed when alternating single and double bonds exist, allowing delocalization of pi electrons across the entire ring. Aromatic systems, on the other hand, possess a fully conjugated structure with a specific number of pi electrons, following Hückel's rule.

To determine the number of pi electrons contributed to the pi system of the heterocyclic ring, count the number of pi electrons associated with each double bond or aromatic ring. Each double bond contributes two pi electrons, while an aromatic ring contributes a total of (4n + 2) pi electrons, where 'n' represents the number of conjugated or aromatic rings. It is important to note that lone pairs of electrons on heteroatoms within the ring do not typically contribute to the pi system.

By summing up the contributions from all the double bonds and aromatic rings within the planar heterocyclic ring, you can determine the total number of electrons contributed to the pi system of the ring.

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find the standard deviation. listed below are the amounts of weight change (in pounds) for 12 women during their first year of work after graduating from college. positive values correspond to women who gained weight and negative values correspond to women who lost weight. 4 -8 14 10 -9 12 -6 1 0 4 -3 9

Answers

The standard deviation of the weight change for these 12 women will be approximately 5.33 pounds

To find the standard deviation of the weight change, we can follow these steps:

Calculate the mean (average) of the weight change values by summing all the values and dividing by the number of observations. In this case, we have 12 women, so the mean is (4 - 8 + 14 + 10 - 9 + 12 - 6 + 1 + 0 + 4 - 3 + 9) / 12 = 28 / 12 = 2.33.

Subtract the mean from each weight change value to obtain the deviations from the mean. For example, for the first woman, the deviation is 4 - 2.33 = 1.67.

Square each deviation obtained in step 2. For the first woman, the squared deviation is (1.67)^2 = 2.79.

Calculate the average of the squared deviations by summing all the squared deviations and dividing by the number of observations. In this case, the sum of squared deviations is (2.79 + 41.44 + 138.67 + 37.44 + 42.11 + 5.33 + 29.44 + 1.11 + 5.33 + 1.44 + 21.33 + 5.33) = 341.26. Dividing this by 12 gives us 341.26 / 12 = 28.44.

Take the square root of the average of squared deviations obtained in step 4. The square root of 28.44 is approximately 5.33.

Therefore, the standard deviation of the weight change for these 12 women is approximately 5.33 pounds. The standard deviation measures the variability or spread of the data points around the mean, indicating how much the weight change values deviate from the average.

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The largest share of national health expenditures is attributed to: A. public health activities. B. net cost of private health insurance. C. structures and equipment. D. personal health care.

Answers

The largest share of national health expenditures is typically attributed to D. personal health care.

What is personal health care?

Personal health care refers to the direct provision of medical goods and services to individuals, including services such as hospital care, physician services, prescription drugs, and other medical supplies. These expenses typically make up the majority of national health expenditures in many countries, including the United States.

Examples of Personal Health Care Services: Personal health care expenditures include costs associated with hospital care (inpatient and outpatient), physician and specialist services, laboratory tests, prescription drugs, medical devices, home health care, nursing home care, and other healthcare services utilized by individuals.

Factors Contributing to Personal Health Care Expenses: Several factors contribute to the high share of national health expenditures attributed to personal health care. These include the increasing prevalence of chronic diseases, advances in medical technology, rising healthcare utilization, and an aging population requiring more healthcare services.

Private Health Insurance: While personal health care expenditures primarily refer to direct payments made by individuals or on their behalf, a significant portion of these costs is covered by private health insurance. Private insurance plans help individuals offset the financial burden of healthcare expenses by pooling risks and providing coverage for various medical services.

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B. use the normaledf function on a calculator to find the probability that the battery life is 20
hours or longer for each phone
algebra 2
unit4 cell phone battery life

Answers

To find the probability that the battery life is 20 hours or longer for each phone using the normcdf function on a calculator, we need the mean and standard deviation of the battery life distribution.

The normcdf function is used to calculate the cumulative probability of a given range in a normal distribution. It requires three inputs: the upper bound, the lower bound, and the mean and standard deviation of the distribution.

Assuming we have the mean (μ) and standard deviation (σ) for each phone's battery life, we can input these values along with the lower bound (20) and a large upper bound (e.g., 10^99) into the normcdf function.

The normcdf function calculates the cumulative probability from the lower bound to the upper bound of a normal distribution. In this case, we are interested in the probability of the battery life being 20 hours or longer, so we use 20 as the lower bound.

By entering the appropriate values into the normcdf  function, the calculator will provide the probability that the battery life is 20 hours or longer for each phone based on their respective mean and standard deviation.

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Shown is a circle with centre O. ABC is a straight line. Angle CBD is 146 degrees

Find the size of angle AOD.

Answers

To find the size of angle AOD, we need additional information. Please provide any relevant angles or measurements associated with angle AOD or any other information that can help determine its size.

An investor buys 1,000 shares of DEF at $40 in a margin account. If the investor wishes to deposit fully paid securities in lieu of cash, what is the minimum market value that the investor must deposit

Answers

The investor must deposit securities with a market value of at least $80,000 in lieu of cash to satisfy the margin requirement. This ensures that the investor maintains the required 50% margin level.

To determine the minimum market value that the investor must deposit in lieu of cash,

we need to consider the margin requirements set by the brokerage firm and the regulations of the relevant securities exchange.

Margin requirements typically specify a minimum margin percentage that must be maintained in the account.

Let's assume that the margin requirement is 50%. This means that the investor must maintain at least 50% of the total value of the investment in the margin account.

Since the investor bought 1,000 shares of DEF at $40 per share,

the total investment value is $40,000

To calculate the minimum market value that the investor must deposit, we divide the total investment value by the margin requirement:

$40,000 / 0.5 = $80,000.

(1,000 shares * $40).

Margin requirements may vary depending on the brokerage firm and the specific security being traded. Investors should always consult their brokerage firm or financial advisor for accurate information on margin requirements and the necessary deposit for their particular investment.

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A company has just paid a dividend of 4.91$. Its discount rate is 8.6%, and the expected perpetual growth rate is 3.6%. What would you expect to be the stock's price TODAY?

Answers

Based on the given dividend of $4.91, a discount rate of 8.6%, and an expected perpetual growth rate of 3.6%, we would expect the stock's price to be $98.20 today.

To determine the stock's price today, we can use the dividend discount model (DDM), also known as the Gordon growth model. The DDM calculates the present value of all future dividends, taking into account the required rate of return and the expected growth rate.

Let's plug in the values given in your question:

Dividend (D) = $4.91

Discount Rate (r) = 8.6% or 0.086

Perpetual Growth Rate (g) = 3.6% or 0.036

Now we can substitute these values into the formula to calculate the stock's price today:

Stock Price =4.91 - 0.086 = 0.036

Stock Price= 0.086−0.036 = 4.91

Simplifying the denominator:

Stock Price = 4.91/0.05

Stock Price=98.20

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What is variance process used for in residential property variance.

Answers

In the context of property variance, a variance refers to a legal authorization or exception granted to a property owner by the local governing authority. It allows the property owner to deviate from specific zoning regulations or land-use restrictions that would otherwise apply to their property.

The variance process is used when property owners believe that strict adherence to the existing regulations would cause undue hardship or prevent them from fully utilizing their property in a way that is reasonable and consistent with neighboring properties.

The purpose of property variances is to address unique circumstances or hardships that may exist for a particular property. Property variances typically involve submitting an application to the local zoning board or planning department, attending public hearings, and providing evidence or arguments to support the need for the variance.

The governing authority evaluates the application based on factors such as the impact on neighboring properties, public health and safety, and the intent of the zoning regulations. If approved, the property owner is granted permission to proceed with the proposed deviation from the regulations.

Overall, property variances provide flexibility in land-use regulations, allowing property owners to find reasonable solutions that meet their specific needs while still considering the broader community interests and objectives of zoning regulations.

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You bought a share of 3 percent preferred stock for $97.06 last year. The market price for your stock is now $99.06. What was your total return for last year

Answers

The total return on the 3 percent preferred stock for last year is $2.00.

To calculate the total return on the preferred stock, we need to consider two components: capital appreciation and dividends received.

The capital appreciation represents the increase in the stock's price over time. In this case, the stock was purchased for $97.06 and its current market price is $99.06. To calculate the capital appreciation, we subtract the initial purchase price from the current market price:

Capital Appreciation = Current Market Price - Purchase Price

= $99.06 - $97.06

= $2.00

Therefore, the capital appreciation of the stock is $2.00.

Preferred stocks typically pay fixed dividends at regular intervals. Since the question does not provide any information about dividends received, we assume that no dividends were paid during the last year. Hence, the dividend component of the total return is zero.

To calculate the total return, we sum up the capital appreciation and dividend components:

Total Return = Capital Appreciation + Dividends

= $2.00 + $0.00

= $2.00

Therefore, the total return for the last year on the 3 percent preferred stock is $2.00.

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why is change management a significant challenge for many organizations during enterprise system implementation?

Answers

Change management is a significant challenge for many organizations during enterprise system implementation due to various factors such as resistance to change, organizational culture, lack of employee engagement, and inadequate communication and training.

Determine the enterprise system implementation?

During enterprise system implementation, organizations typically undergo significant changes in processes, roles, and technologies. This can lead to resistance from employees who may be accustomed to existing ways of working. Resistance to change can hinder the adoption and utilization of the new system, affecting its success.

Organizational culture also plays a role. If the organization has a rigid or hierarchical culture that is resistant to change or lacks a culture of innovation and learning, it becomes difficult to implement and integrate the new system effectively.

Lack of employee engagement and involvement in the implementation process can further impede change. Employees need to understand the reasons behind the change, how it will benefit them and the organization, and be provided opportunities for input and feedback.

Inadequate communication and training can be a major obstacle. Employees must be informed about the changes, their roles and responsibilities, and be provided with sufficient training to effectively use the new system. Insufficient communication and training can lead to confusion, frustration, and resistance.

Overall, change management is crucial during enterprise system implementation to address these challenges and ensure a smooth transition, user acceptance, and successful adoption of the new system.

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3. Above are pictures of a regular pyramid and prism, both with square bases. One side of the
base of the pyramid has a length of 10 inches, one side of the base of the prism has a length of
10 inches, both solids have a height of 12 inches. The pyramid has a slant height of 13 inches.
Show ALL your work!
a. Which one has the larger surface area and by how much?
b. Which has the larger volume and by how much?

Answers


Let's calculate the surface area and volume for both the pyramid and the prism and compare the results.

a. Surface Area:

The surface area of a regular pyramid is given by the formula:

SA_pyr = Base Area + (1/2) * Perimeter of Base * Slant Height

The base area of the pyramid is the area of a square, which is equal to one side length squared:

Base Area_pyr = (10 inches)² = 100 square inches

The perimeter of the base is the sum of all four sides:

Perimeter of Base_pyr = 4 * 10 inches = 40 inches

Plugging the values into the formula, we have:

SA_pyr = 100 square inches + (1/2) * 40 inches * 13 inches
SA_pyr = 100 square inches + 20 inches * 13 inches
SA_pyr = 100 square inches + 260 square inches
SA_pyr = 360 square inches

Now, let's calculate the surface area of the prism. The surface area of a prism with a square base is given by the formula:

SA_prism = 2 * Base Area + Perimeter of Base * Height

The base area of the prism is the area of a square, which is equal to one side length squared:

Base Area_prism = (10 inches)² = 100 square inches

Plugging the values into the formula, we have:

SA_prism = 2 * 100 square inches + 40 inches * 12 inches
SA_prism = 200 square inches + 480 square inches
SA_prism = 680 square inches

Therefore, the pyramid has a surface area of 360 square inches, and the prism has a surface area of 680 square inches.

The prism has a larger surface area by:
680 square inches - 360 square inches = 320 square inches.

b. Volume:

The volume of a regular pyramid is given by the formula:

V_pyr = (1/3) * Base Area * Height

Plugging the values into the formula, we have:

V_pyr = (1/3) * 100 square inches * 12 inches
V_pyr = 400 cubic inches

The volume of a prism with a square base is given by the formula:

V_prism = Base Area * Height

Plugging the values into the formula, we have:

V_prism = 100 square inches * 12 inches
V_prism = 1200 cubic inches

Therefore, the pyramid has a volume of 400 cubic inches, and the prism has a volume of 1200 cubic inches.

The prism has a larger volume by:
1200 cubic inches - 400 cubic inches = 800 cubic inches.

To summarize:

a. The prism has a larger surface area by 320 square inches.
b. The prism has a larger volume by 800 cubic inches.

skating rink a rectangular skating rink measures 40 m by 20 m. it is . to be doubled in area by extending each side by the same amount. determine how much each side should be extended, to the nearest tenth of a metre.

Answers

Each side of the skating rink should be extended by approximately 3.2 meters to double the area.

What is extending sides?

Extending sides refers to the process of increasing the length or width of an object or structure, typically by adding additional length or width to one or more sides. This extension can be done to increase the overall size, area, or dimensions of the object.

To double the area of the rectangular skating rink, we need to extend each side by the same amount. Let's denote the extension length as "x" meters.

The original area of the skating rink is given by length multiplied by width: 40 m * 20 m = 800 square meters.

To double the area, we want the new area to be 2 times the original area: 2 * 800 = 1600 square meters.

After extending each side by "x" meters, the new length will be (40 + x) meters and the new width will be (20 + x) meters.

The new area can be calculated as the product of the new length and width: (40 + x) * (20 + x) square meters.

Setting the new area equal to 1600 square meters, we have the equation:

(40 + x) * (20 + x) = 1600

Expanding the equation, we get:

[tex]800 + 40x + 20x + x^2 = 1600[/tex]

Simplifying and rearranging, we have:

[tex]x^2 + 60x - 800 = 0[/tex]

Now we can solve this quadratic equation to find the value of "x" using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

[tex]x = (-b \pm \sqrt{(b^2 - 4ac)) / (2a)[/tex]

For our equation, a = 1, b = 60, and c = -800. Substituting these values into the quadratic formula, we get:

[tex]x = (-60 \± \sqrt{(60^2 - 4 * 1 * -800)) / (2 * 1)[/tex]

Simplifying further:

[tex]x = (-60 \± \sqrt{(3600 + 3200)) / 2[/tex]

[tex]x = (-60 \± \sqrt{(6800)) / 2[/tex]

[tex]x = (-60 \± \sqrt{(2^3 * 5^2 * 17)) / 2[/tex]

[tex]x = (-60 \± 2\sqrt{(85)) / 2[/tex]

[tex]x = -30 \± \sqrt{(85)[/tex]

Since we are looking for a positive extension length, we take the positive square root:

[tex]x = -30 + \sqrt{(85)x \approx 3.2[/tex]

Therefore, each side of the skating rink should be extended by approximately 3.2 meters to double the area.

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NUMBER SENSE Events A and B are independent. Suppose P(B)=0.4 and P(A and B)=0.13 . Find P(A) .

Answers

The probability of event A (P(A)) is approximately 0.325.

To find the probability of event A (P(A)), we can use the formula for the probability of the intersection of two independent events:

P(A and B) = P(A) * P(B)

Given that P(B) = 0.4 and P(A and B) = 0.13, we can substitute these values into the formula:

0.13 = P(A) * 0.4

Now, we can solve for P(A) by isolating it:

P(A) = 0.13 / 0.4

Performing the division, we find:

P(A) ≈ 0.325

Therefore, the probability of event A (P(A)) is approximately 0.325.

It's important to note that in this scenario, events A and B are assumed to be independent. This means that the occurrence of event A does not affect the probability of event B, and vice versa.

What is probability means?

A probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

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Chantal started the day with 50 dollars. in the afternoon, her friend returned the 32 dollars he borrowed. she spent 40 dollars at the grocery
store that evening.
which expression can be used to find the amount of money chantal has at the end of the day?
a 50 -- 32 + 40
b. 50 - 32 - 40
c. 50 - (-32) + 40
d. 50 - (-32) - 40

Answers

Answer:

Option d

Step-by-step explanation:

Because when it comes to integers there is rule in subtraction that is a-(-d)=a+d=j.

Therefore 50- (-32) - 40

=50 + 32 - 40

=82 - 40

=42

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Which equation represents a line that has a slope of 3 and goes through the point (-3,7)

Answers

Answer:

y + 3 = 3(x - 7)

Step-by-step explanation:

Plugging in the slope and points

Point slope form is  y - y1 = m(x - x1)

y - (-3) = (3)(x - (7))

y + 3 = 3(x-7)

The drug ________ would be expected to inhibit/decrease aggression. haloperidol cocaine methysergide fluoxetine (Prozac)

Answers

The drug fluoxetine (Prozac) would be expected to inhibit/decrease aggression.

What is fluoxetine Prozac used for?

Fluoxetine is a type of antidepressant known as a selective serotonin reuptake inhibitor (SSRI). It is more effect on the mental health and physical state of mind. This type of drug also stops the working of mind and less work of mind. Drugs are very harmful for our body.

There is some Side Effects of drugs are:

Headache, nausea, diarrhea, dry mouth, increased sweating, and so on.

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How to graph y=x^2+6x+7 on a quadratic graph​

Answers

The graph of the function y = x²+ 6x + 7 is given in the attachment.

To graph the quadratic function y = x²+ 6x + 7:

Find the vertex using the formula -b/(2a), where a is the coefficient of x²and b is the coefficient of x.

The vertex will be at (-3, -2).

Plot the vertex (-3, -2) on the graph.

Choose additional x-values and calculate the corresponding y-values by substituting them into the equation.

Plot these points on the graph.

Connect the plotted points smoothly to form a U-shaped curve, which represents the parabola.

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help pls thank you very much!

Answers

Answer:

please see answers below

Step-by-step explanation:

In a right-angled triangle, a ² + b ² = c ²

Sine rule:   a/SIN A  =  b/SIN B  =   c/SIN C

x/sin 90 = 8/sin 45

x = (8 sin 90) / sin 45

= 8√2

y² = x² - 8²

= ( 8√2)² - 64

= 128 - 64

= 64.

y = √64 = 8

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